Skip to Main content Skip to Navigation
Journal articles

On the expressive power of temporal logic for finite words

Abstract : We study the expressive power of linear propositional temporal logic interpreted on finite sequences or words. We first give a transparent proof of the fact that a formal language is expressible in this logic if and only if its syntactic semigroup is finite and aperiodic. This gives an effective algorithm to decide whether a given rational language is expressible. Our main result states a similar condition for the "restricted" temporal logic (RTL), obtained by discarding the until operator. A formal language is RTL-expressible if and only if its syntactic semigroup is finite and satisfies a certain simple algebraic condition. This leads to a polynomial time algorithm to check whether the formal language accepted by an n-state deterministic automaton is RTL-expressible.
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-00020069
Contributor : Jean-Eric Pin <>
Submitted on : Saturday, March 4, 2006 - 4:15:51 PM
Last modification on : Friday, March 27, 2020 - 3:31:32 AM
Document(s) archivé(s) le : Saturday, April 3, 2010 - 10:42:00 PM

Identifiers

Citation

Joelle Cohen, Dominique Perrin, Jean-Eric Pin. On the expressive power of temporal logic for finite words. Journal of Computer and System Sciences, Elsevier, 1993, 46, pp.271-294. ⟨10.1016/0022-0000(93)90005-H⟩. ⟨hal-00020069⟩

Share

Metrics

Record views

559

Files downloads

364